Question

ajutatima va rog mult clik pe poza

Answer 1

       
$6a)\\ 11x-44\ \textless \ 0 \\ 11x\ \textless \ 44 \\ x\ \textless \ \frac{44}{11} \\ x\ \textless \ 4 \\ x\in \{-1;\;0;\;1;\;2;\;3\} \\ \\ 6b) \\ -7+6x\ \textless \ 4x+15 \\ 6x-4x\ \textless \ 15+7 \\ 2x\ \textless \ 22 \\ x\ \textless \ \frac{22}{2} \\ x\ \textless \ 11 \\ x \in \{-1;\;0;\;1;\;2;\;3;\;4;\;5;\;6;\;7;\;8;\;9;\;10\}$

$6c) \\ x-17 \geq 4x-5 \\ x-4x \geq -5+17 \\ -3x \geq 12 \;\;\;\;\; |*(-1)\\ 3x \leq -12 \\ x \leq \frac{-12}{3} \\ x \leq -4 \;si\;x\ \textgreater \ -1\;=\ \textgreater \ \;x \in \Phi$

$6d) \\ 2x\ \textgreater \ 3(x-1) \\ 2x\ \textgreater \ 3x-3 \\ 2x-3x\ \textgreater \ -3 \\ -x\ \textgreater \ -3\;\;\;\;\;|*(-1) \\ x\ \textless \ 3 \; si \; x \geq -1 \\ x \in \{-1;\;0;\;1;\;2 \} \\ \\ 6e) \\ 2x-6+3x \leq 14 \\ 5x \leq 14 + 6 \\ 2x-6+3x \leq 14 \\ 5x \leq 20 \\x \leq \frac{20}{5} \\ x \leq 4 \;\;\;=\ \textgreater \ \;\;\;x \in \{-1; \;0;\;1;\;2;\;3;\;4\}$

$6f) \\ 8x+20\ \textless \ 3x \\ 8x-3x\ \textless \ -20 \\ 5x\ \textless \ -20 \\ x\ \textless \ \frac{-20}{5} \\ x\ \textless \ -4\;\;\;si\;\;\;x \geq -1 \\ =\ \textgreater \ x \in \Phi$

$6g) \\ 3(x-3) \leq 4(2x+1)-3 \\ 3x-9 \leq 8x+4-3 \\ 3x-8x \leq 4-3+9 \\ -5x \leq 10 \\ x \leq \frac{10}{5} \\ x \leq 2\\ x \in \{-1;\;0;\;1;\;2\}$

$6h) \\ (5- \sqrt{7})x+5 \leq \sqrt{7} \\ (5- \sqrt{7})x \leq \sqrt{7}-5 \\ (5- \sqrt{7})x \leq -(5-\sqrt{7}) \\ x \leq \frac{-(5-\sqrt{7})}{(5- \sqrt{7})} \\ x \leq -1 \;\;\;si\;\;\;x \geq -1 \\ x \in\{-1\} \;\;=\ \textgreater \ \;\;x=-1$

$6i) \\ \sqrt{3} x+4 \leq 1-2\sqrt{3} x \\ \sqrt{3}x+ 2\sqrt{3} x \leq 1-4 \\ 3\sqrt{3}x \leq -3 \\ x \leq \frac{-3 }{3\sqrt{3}} \\ x \leq -\frac{1 }{\sqrt{3}} \\ x \leq -\frac{\sqrt{3} }{3} \\ x \leq -0,577 \;\;\;si \;\;\; x \geq -1\;\;\; si \;\;\; x \in Z \\ =\ \textgreater \ \;\;\;x \in \{-1\}\;\;\;=\ \textgreater \ \;\;x=-1$